Related papers: Second-Order Asymptotics of Hoeffding-Like Hypothe…
In this paper we initiate the study of $2$nd order variational problems in $L^\infty$, seeking to minimise the $L^\infty$ norm of a function of the hessian. We also derive and study the respective PDE arising as the analogue of the…
Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to…
Standard high-dimensional factor models assume that the comovements in a large set of variables could be modeled using a small number of latent factors that affect all variables. In many relevant applications in economics and finance,…
We consider the task of distinguishing between two different alternative models that can roughly equally explain observed time series data, mainly focusing on the period ambiguity case (aliasing). We propose a test for checking whether the…
Generative models have achieved remarkable success across a range of applications, yet their evaluation still lacks principled uncertainty quantification. In this paper, we develop a method for comparing how close different generative…
We study the problem of closeness testing for continuous distributions and its implications for causal discovery. Specifically, we analyze the sample complexity of distinguishing whether two multidimensional continuous distributions are…
We study a distributed binary hypothesis testing (HT) problem with communication and security constraints, involving three parties: a remote sensor called Alice, a legitimate decision centre called Bob, and an eavesdropper called Eve, all…
Given an input query, generative models such as large language models produce a random response drawn from a response distribution. Given two input queries, it is natural to ask if their response distributions are the same. While…
We study concentration inequalities for the Kullback--Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes…
In statistical classification/multiple hypothesis testing and machine learning, a model distribution estimated from the training data is usually applied to replace the unknown true distribution in the Bayes decision rule, which introduces a…
We study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and…
We revisit the distributed hypothesis testing (or hypothesis testing with communication constraints) problem from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized…
We introduce two novel non-parametric statistical hypothesis tests. The first test, called the relative test of dependency, enables us to determine whether one source variable is significantly more dependent on a first target variable or a…
The double hypothesis test (DHT) is a test that allows controlling Type I (producer) and Type II (consumer) errors. It is possible to say whether the batch has a defect rate, p, between 1.5 and 2%, or between 2 and 5%, or between 5 and 10%,…
Many practical studies rely on hypothesis testing procedures applied to data sets with missing information. An important part of the analysis is to determine the impact of the missing data on the performance of the test, and this can be…
A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…
We consider the problems of hypothesis testing on a probability measure of independent sample, on solution of ill-posed problem, on deconvolution problem and on Poisson mean measure. For all these setups necessary conditions and sufficient…
Kullback-Leibler (KL) divergence is one of the most important divergence measures between probability distributions. In this paper, we prove several properties of KL divergence between multivariate Gaussian distributions. First, for any two…
This paper investigates improved testing inferences under a general multivariate elliptical regression model. The model is very flexible in terms of the specification of the mean vector and the dispersion matrix, and of the choice of the…
Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual…